Abstract: | Summary Let the random variablesX
1,X
2, ...,X
n
be generated by the first-order autoregressive modelX
i
=θX
i−1
+e
i
wheree
i
,i=1, 2, ...,n, are i.i.d. random variables with mean zero, variance σ2, and with unspecified density functiong(·). In the present paper we obtain a characterization of limiting distributions of nonparametric and parametric estimators
of θ as well as a local asymptotic minimax bound of the risks of estimators. |